设向量组a1,a2,a3线性无关,又 b1=a1-a2, b2=2a1+a2+3a3, b3=3a1+a2+2a3, 讨论向量组b1,b2,b3的线性相关性.

设0=k1b1+k2b2+k3b3
=k1(a1-a2)+k2(2a1+a2+3a3)+k3(3a1+a2+2a3)
=(k1+2k2+3k3)a1+(-k1+k2+k3)a2+(3k2+2k3)a3
a1,a2,a3线性无关，
k1+2k2+3k3=0
-k1+k2+k3=0
3k2+2k3=0
解得k1=k2=k3=0
b1,b2,b3线性无关本回答被提问者采纳